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Norton, Anderson; Ulrich, Catherine; Kerrigan, Sarah – Journal for Research in Mathematics Education, 2023
This article introduces unit transformation graphs (UTGs) as a tool for diagramming the ways students use sequences of mental actions to solve mathematical tasks. We report findings from a study in which we identified patterns in the ways preservice elementary school teachers relied on working memory to coordinate mental actions when operating in…
Descriptors: Graphs, Fractions, Short Term Memory, Preservice Teachers
Supovitz, Jonathan A.; Ebby, Caroline B.; Remillard, Janine T.; Nathenson, Robert – Journal for Research in Mathematics Education, 2021
In this article, we use a two-dimensional assessment to examine the experimental impacts of a mathematics learning trajectory-oriented formative assessment program on student strategies for problems involving multiplication and division. Working from the theory that the development of students' multiplicative reasoning involves improvements in…
Descriptors: Accuracy, Problem Solving, Mathematics Instruction, Formative Evaluation
Hackenberg, Amy J.; Lee, Mi Yeon – Journal for Research in Mathematics Education, 2015
To understand relationships between students' fractional knowledge and algebraic reasoning in the domain of equation writing, an interview study was conducted with 12 secondary school students, 6 students operating with each of 2 different multiplicative concepts. These concepts are based on how students coordinate composite units. Students…
Descriptors: Secondary School Mathematics, Equations (Mathematics), Mathematics Skills, Multiplication
Whitacre, Ian; Nickerson, Susan D. – Journal for Research in Mathematics Education, 2016
This study examines how collective activity related to multiplication evolved over several class sessions in an elementary mathematics content course that was designed to foster prospective elementary teachers' number-sense development. We document how the class drew on as-if-shared ideas to make sense of multidigit multiplication in terms of…
Descriptors: Preservice Teachers, Multiplication, Elementary School Teachers, Elementary School Mathematics

Christou, Constantinos; Philippou, George – Journal for Research in Mathematics Education, 1998
Investigates the effect of mental schemes corresponding to additive and multiplicative situations in the process of interpreting and solving problems. Classifies relative difficulties of problems according to their situations which are considered through a written test administered to pupils in grades 2, 3, and 4. Supports the assumption that…
Descriptors: Addition, Arithmetic, Cognitive Development, Concept Formation

Fischbein, Efraim; And Others – Journal for Research in Mathematics Education, 1985
Over 600 pupils in grades five, seven, and nine in Italian schools were asked to choose the operation needed to solve 26 multiplication and division word problems. The findings seemed to confirm the impact of the repeated addition model on multiplication and of the partitive model on division. (MNS)
Descriptors: Cognitive Processes, Computation, Division, Educational Research

Kouba, Vicky L. – Journal for Research in Mathematics Education, 1989
Classifies children's solution strategies by degree of abstraction and by use of physical objects. Children in grades one, two, and three were given two multiplication and four division word problems that differed in semantic structure. (Author/YP)
Descriptors: Division, Elementary School Mathematics, Mathematical Concepts, Mathematics Achievement

Greer, Brian – Journal for Research in Mathematics Education, 1987
Investigated was how easily pupils aged 12 and 13 who were initially unaware of the invariance of an operation (with decimals) modeling a situation could be led to such awareness. Results from clinical interviews are reviewed and a protocol presented. It appeared difficult to induce conservation. (MNS)
Descriptors: Cognitive Processes, Conservation (Concept), Decimal Fractions, Division

Sellke, Donald H.; And Others – Journal for Research in Mathematics Education, 1991
This study tested the effectiveness of an experimental instructional strategy for writing arithmetic sentences for simple multiplication and division story problems involving nonintegral factors. Significant effects in favor of the experimental group were found on an intermediate test and a posttest. (Author/CW)
Descriptors: Arithmetic, Division, Equations (Mathematics), Junior High Schools

Carpenter, Thomas P.; And Others – Journal for Research in Mathematics Education, 1993
After a year of instruction, 70 kindergarten children were individually interviewed as they solved basic, multistep, and nonroutine word problems. Thirty-two used a valid strategy for all 9 problems, and 44 correctly answered 7 or more problems. Modeling provided a unifying framework for thinking about problem solving. (Author/MDH)
Descriptors: Addition, Cognitive Processes, Cognitive Style, Division